(p+1)(p+1)=51

Solution for (p+1)(p+1)=51 equation:

(p+1)(p+1)=51

We move all terms to the left:

(p+1)(p+1)-(51)=0

We multiply parentheses ..

(+p^2+p+p+1)-51=0

We get rid of parentheses

p^2+p+p+1-51=0

We add all the numbers together, and all the variables

p^2+2p-50=0

a = 1; b = 2; c = -50;
Δ = b2-4ac
Δ = 22-4·1·(-50)
Δ = 204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{51}}{2*1}=\frac{-2-2\sqrt{51}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{51}}{2*1}=\frac{-2+2\sqrt{51}}{2}
$